Solve for $x$ and $y$ using elimination. ${2x+y = 22}$ ${3x-y = 23}$
Answer: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $y$ and $-y$ cancel out. $5x = 45$ $\dfrac{5x}{{5}} = \dfrac{45}{{5}}$ ${x = 9}$ Now that you know ${x = 9}$ , plug it back into $\thinspace {2x+y = 22}\thinspace$ to find $y$ ${2}{(9)}{ + y = 22}$ $18+y = 22$ $18{-18} + y = 22{-18}$ ${y = 4}$ You can also plug ${x = 9}$ into $\thinspace {3x-y = 23}\thinspace$ and get the same answer for $y$ : ${3}{(9)}{ - y = 23}$ ${y = 4}$